论文标题
矿石本地化中的建设性算术享受足够的通勤性
Constructive Arithmetics in Ore Localizations Enjoying Enough Commutativity
论文作者
论文摘要
本文继续进行了一项研究计划，该计划对我们以前的论文启动的非交通矿石定位的建设性研究，尤其触及了此类本地化中算术的建设性。早些时候，我们引入了域的本体定位，几何和理性的类型，作为我们研究的对象。在这里，我们将此分类扩展到具有零除外的环，并考虑到足够交换的上述类型的矿石集：这样的集合要么属于交换代数，要么是中心的，或者是核心的元素。通过使用以前开发的系统方法，我们证明了交换性多项式代数的定位中的算术是建设性的，并提供了必要的算法。我们还解决了计算理想局部封闭的重要问题，该理想也称为降低，并为计算交换环中给定理想的符号能力提供了一种算法。我们还提供算法来计算以足够的换击性相对于矿石集的某些非交通环的局部封闭。
This paper continues a research program on constructive investigations of non-commutative Ore localizations, initiated in our previous papers, and particularly touches the constructiveness of arithmetics within such localizations. Earlier we have introduced monoidal, geometric and rational types of localizations of domains as objects of our studies. Here we extend this classification to rings with zero divisors and consider Ore sets of the mentioned types which are commutative enough: such a set either belongs to a commutative algebra or it is central or its elements commute pairwise. By using the systematic approach we have developed before, we prove that arithmetic within the localization of a commutative polynomial algebra is constructive and give the necessary algorithms. We also address the important question of computing the local closure of ideals which is also known as the desingularization, and present an algorithm for the computation of the symbolic power of a given ideal in a commutative ring. We also provide algorithms to compute local closures for certain non-commutative rings with respect to Ore sets with enough commutativity.
